Control and Optimization in Applied Mathematics

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Analyzing Drug Therapy on the Interaction Between Tumor and Immune Cells Based on Optimal Fractional Control Theory

Articles in Press

Document Type : Research Article

Authors

1 Faculty of Mathematics‎, ‎Shiraz University of Technology‎, ‎Shiraz‎, ‎Iran.

2 ABlauw-roodlaan 15‎, ‎2718 JN‎, Zoetermeer‎, ‎Netherlands.

3 Department of Mathematics‎, Jahrom University‎, ‎Iran‎.

10.30473/coam.2025.72347.1263

Abstract

Cancer is a class of diseases characterized by uncontrolled cell growth that affects immune cells‎. ‎There are several treatment options available‎, ‎including surgery‎, ‎chemotherapy‎, ‎hormonal therapy‎, ‎radiation therapy‎, ‎targeted therapy‎, ‎and palliative care‎. ‎Among these‎, ‎chemotherapy is one of the most widely used and recognized methods‎. ‎This paper‎ presents a novel model designed to control cancer cell growth based on a system of nonlinear fractional differential equations with delay in chemotherapy‎. ‎The model focuses on the competition between tumor and immune cells to minimize the number of tumor cells and determine the optimal dosage of the administered drug‎. ‎It can simulate various scenarios and predict the outcomes of different chemotherapy regimens‎. ‎By employing discretization and the Grunwald-Letnikov method‎, ‎we aim to gain insights into why some patients respond well to chemotherapy while others do not‎. ‎The results may also help identify potential drug targets and optimize existing treatments‎.

Highlights

  • Introduced a novel framework using nonlinear fractional differential equations for accurate simulation of cancer cell growth.
  • Developed a time-delay model to investigate the competitive dynamics between immune and tumor cells.
  • Achieved optimization of drug dosage personalized to individual patient responses, improving treatment outcomes.
  • Utilized the Grunwald-Letnikov method to effectively predict diverse patient responses to chemotherapy.

Keywords

Main Subjects

References
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Control and Optimization in Applied Mathematics

Articles in Press, Accepted Manuscript
Available Online from 21 February 2025
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